10

INFORMATION FOR STUDENTS

# Example 2

Sample CAHSEE Question

12

x

5

What is the value of x in the triangle shown above?

A

11

B

13

C

17

# D 169

M02446

Solution Here is a geometry question and a chance for making a visual estimate. You could use the Pythagorean theorem to solve the problem, but you don’t have to. Look at the diagram. If it helps, you can make a “paper ruler” out of part of your booklet and use it to measure the diagram.

The length x has to be more than 12. But no way is it 169. So the answer is either 13 or 17. (You just eliminated options A and D!) But notice: 17 is the total distance along the two legs, 12 5. Segment x must be shorter than that, because it goes straight. So the correct answer is B.

Is it cheating to choose an answer without actually computing it? NO. It’s demonstrating what you know and what you can do on a multiple- choice exam.

The test makers care that you know how big numbers are, that you understand variables, and that you can reason about geometric figures. They care that you know the basics well. But it’s not so important whether you can do complicated arithmetic with paper and pencil.

Should you know how to compute the answer? Of course you should, and there will be many questions where you will have to compute or do some algebra to tell which answer is correct. But if you get stumped, some of these strategies might help you get a question correct.